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Wavelets and MERA

Some of the key insights that led to the
development of DMRG stemmed from studying the behavior of real space RG for
single particle wavefunctions, a much simpler context than the many-particle
case of main interest. Similarly, one
can gain insight into MERA by studying wavelets. I will introduce basic wavelet theory and
show how one of the most well-known wavelets, a low order orthogonal wavelet of
Daubechies, can be realized as the fixed point of a specific MERA (in
single-particle direct-sum space).
Higher order wavelets and the conflict between compactness in real and
Fourier space may provide insight into generalized MERAs for many particle
systems.